Summary: Don't put that notch on your Gospel gun until you are sure you hit the target. If it is not a heart shot, a flesh wound will kill them.
"A man convinced against his will is of the same opinion still." - Unknown
Something to be remembered when evangelizing. Just because they say a prayer on the doorstep does not mean they are saved. They may be just trying to get you off their doorstep or saying the prayer to hedge their bets while still maintaining their core beliefs. I am positive that many souls that have been reported as won will be in Hell unless they were truly won later than the time they were reported.
Matt 23:15 Woe unto you, scribes and Pharisees, hypocrites! for ye compass sea and land to make one proselyte, and when he is made, ye make him twofold more the child of hell than yourselves
If there is no lasting fruit, albeit small, you have inoculated the person thinking they are saved and made them sealed to Hell, nor Heaven or at best made the next soul winner's work harder as they have to lead them out of a false conversion into a true one.
I saw much of this in the soul winning while an IFB. Folks would come back from an door-to-door evangelism time saying how many were saved yet the people never came to church, were never baptized and often would not even open the door on a follow up visit or if they did, they made excuses and shut the door as quickly as possible.
I have had many people say the prayer in my ministry, especially in jail, but I cannot say with any certainty that any of them were truly saved. On God knows how many He won through me and how many I sealed to Hell by inoculation. My only hope is where I erred, He sent someone else to clean up my mess and truly win them.
So be careful and be sure you are going in the Spirit and He gives you discern on how to deal with each person and discern when to press on to the prayer or wait until another day. Maranatha!